Solve x^2 x(6-2x)

Question

Simplify the expression

6 x^{3} - 2 x^{4}

Evaluate

x^{2} \times x (6 - 2 x)

Multiply the terms with the same base by adding their exponents

x^{2 + 1} (6 - 2 x)

Add the numbers

x^{3} (6 - 2 x)

Apply the distributive property

x^{3} \times 6 - x^{3} \times 2 x

Use the commutative property to reorder the terms

6 x^{3} - x^{3} \times 2 x

Solution

More Steps

Evaluate

x^{3} \times 2 x

Use the commutative property to reorder the terms

2 x^{3} \times x

Multiply the terms

More Steps

Evaluate

x^{3} \times x

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{3 + 1}

Add the numbers

x^{4}

2 x^{4}

6 x^{3} - 2 x^{4}

Show Solution

2 x^{3} (3 - x)

Evaluate

x^{2} \times x (6 - 2 x)

Multiply the terms with the same base by adding their exponents

x^{2 + 1} (6 - 2 x)

Add the numbers

x^{3} (6 - 2 x)

Factor the expression

x^{3} \times 2 (3 - x)

Solution

2 x^{3} (3 - x)

Show Solution

x_{1} = 0, x_{2} = 3

Evaluate

x^{2} \times x (6 - 2 x)

To find the roots of the expression,set the expression equal to 0

x^{2} \times x (6 - 2 x) = 0

Multiply

More Steps

Multiply the terms

x^{2} \times x (6 - 2 x)

Multiply the terms with the same base by adding their exponents

x^{2 + 1} (6 - 2 x)

Add the numbers

x^{3} (6 - 2 x)

x^{3} (6 - 2 x) = 0

Separate the equation into 2 possible cases

x^{3} = 0 6 - 2 x = 0

The only way a power can be 0 is when the base equals 0

x = 0 6 - 2 x = 0

Solve the equation

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Evaluate

6 - 2 x = 0

Move the constant to the right-hand side and change its sign

- 2 x = 0 - 6

Removing 0 doesn't change the value,so remove it from the expression

- 2 x = - 6

Change the signs on both sides of the equation

2 x = 6

Divide both sides

\frac{2 x}{2} = \frac{6}{2}

Divide the numbers

x = \frac{6}{2}

Divide the numbers

More Steps

Evaluate

\frac{6}{2}

Reduce the numbers

\frac{3}{1}

Calculate

3

x = 3

x = 0 x = 3

Solution

x_{1} = 0, x_{2} = 3

Show Solution